We study a unilateral equilibrium problem for the
energy functional of a lipid tubule subject
to an external field. These tubules, which constitute many biological systems,
may form
assemblies when they are brought in contact, and so made to adhere to one
another along
at interstices. The contact energy is taken to be proportional to the area
of contact through
a constant, which is called the adhesion potential.
This competes against the external field
in determining the stability of patterns with flat interstices. Though the
equilibrium problem
is highly nonlinear, we determine explicitly the stability diagram for
the adhesion between
tubules. We conclude that the higher the field, the lower the adhesion
potential needed to
make at interstices energetically favourable, though its critical value
depends also on the
surface tension of the interface between the tubules and the isotropic
fluid around them.